hi could you please help solve exercise 5.13? **Exercise 5.12** A digital \( (K, t) \) call option gives its holder 1 at expiration time \( t \) if \( S(t) \geq K \), or 0 if \( S(t) < K \). A digital \( (K, t) \) put option gives its holder 1 at expiration time \( t \) if \( S(t) < k \), or 0 if \( S(t) \geq K \). Let \( C_1 \) and \( C_2 \) be the costs of such digital call and put options on the same security. Derive a put-call parity relationship between \( C_1 \) and \( C_2 \).**Exercise 5.13** A European call and put option on the same security both expire in three months, both have a strike price of 20, and both sell for the price 3. If the nominal continuously compounded interest rate is 10% and the stock price is currently 25, identify an arbitrage.**Exercise 5.14** Let \( C_a \) and \( P_a \) be the costs of American call and put options (respectively) on the same security, both having the same strike price \( K \) and exercise time \( t \). If S is the present price of the security, give either an identity or an inequality that relates the quantities \( C_a, P_a, K, S, \) and \( e^{-rt} \). Briefly explain.**Exercise 5.15** Consider two put options on the same security, both of which have expiration \( t \). Suppose the exercise prices of the two puts are \( K_1 \) and \( K_2 \), where \( K_1 > K_2 \). Argue that...

Name: hi could you please help solve exercise 5.13? **Exercise 5.12** A dig
Uploaded: 2024-03-20T07:07:37.000Z
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Description: hi could you please help solve exercise 5.13? **Exercise 5.12** A digital \( (K, t) \) call option gives its holder 1 at expiration time \( t \) if \( S(t) \geq K \), or 0 if \( S(t) < K \). A digital \( (K, t) \) put option gives its holder 1 at ex